In terms of keypoint descriptors, a number of 2D descriptors have been proposed, generally based on local image gradient orientation information, including gradient orientation [1]}, ORB [2]}, BRIEF [3]}, typically these have not been extended to 3D. Rank-order normalization has been shown to improve upon standard 2D gradient descriptors [4]}. Deep learning has been used to extract keypoints and descriptors, learned invariant feature transform (LIFT) [5]}, DISK [6]}, LF-Net [7]}, SuperPoint [8]}, Hardnet  [9]}. Surprisingly, variants of the original SIFT histogram descriptor including SIFT-Rank [10]}, DSP-SIFT [11]} or RootSIFT [12]} are still competitive in terms of keypoint matching performance [13]}, [14]}, particularly for non-planar objects and image retrieval [15]}. SIFT keypoint extraction is based solely on fundamental, symmetric and uniform mathematical operators, e.g. the Gaussian, Laplacian, and uniformly sampled gradient operators. The resulting keypoints thus represent a class of highly informative patterns that are invariant to image scaling and rotation in addition to translation, and may be identified in any context with no explicit training procedure and nor bias towards specific training datasets used.
